Haley, who will step down as UN ambassador at the end of the year, has repeatedly accused the United Nations of having an anti-Israel bias and strongly supports Israel in its latest confrontation with Hamas in Gaza.
If adopted, it would mark the first time the assembly has taken aim at Hamas, the Islamist militant group that has ruled the Gaza Strip since 2007.
The United States has won crucial backing from the European Union, with all 28 countries set to support the US measure that condemns Hamas for firing rockets into Israel and demands an end to the violence.
But diplomats said the US draft resolution was unlikely to win the two-thirds majority required for adoption in the 193-nation assembly.
The Palestinians sought to thwart the US move by presenting an amendment to the US text to include a reference to UN resolutions that condemn Israeli settlements, call for negotiations on East Jerusalem and pledge support for the two-state solution.
After talks with the Europeans late Wednesday, the Palestinians agreed to withdraw their amendment and instead table a separate resolution, diplomats said.
That draft resolution calls "for the achievement, without delay, of a comprehensive, just and lasting peace in the Middle East" based on UN resolutions.
In negotiations with the Europeans, the United States agreed to add a mention of "relevant UN resolutions" in its draft, but without specifying which ones. The US text does not refer specifically to the two-state solution.
The European Union, like the United States, considers Hamas a terror group. EU countries will support both draft resolutions, according to diplomats.
- US takes vote seriously -
Haley rattled the United Nations when she arrived in January 2017 vowing that the United States will be "taking names" of countries that oppose President Donald Trump's foreign policy.
Ahead of the vote, the US ambassador sent a letter to all UN missions to make clear that "the United States takes the outcome of this vote very seriously."
The vote at the assembly comes as Haley prepares to step away from public life even as polls show she remains one of the most popular members of Trump's cabinet.
"She would like to go out with something," said a Security Council diplomat of the US-drafted resolution.
Resolutions adopted by the General Assembly are non-binding, but they carry political weight and are seen as a barometer of world opinion.
The United States put forward the resolution as it prepares to unveil new peace proposals that the Palestinians have already rejected.
The Palestinians have severed ties with the Trump administration after the decision a year ago to move the US embassy to Jerusalem and declare the city Israel's capital.
The US administration has also cut more than $500 million in Palestinian aid.
The Palestinians see East Jerusalem as the capital of their future state. International consensus has been that Jerusalem's status must be negotiated between the two sides.
The assembly session is scheduled to begin at 3:00 pm (2000 GMT).